Shallowtone: Difference between revisions
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The name was coined by [[User:CompactStar|CompactStar]] in 2024. It refers to how it is an opposite to [[deeptone]] (which is on the other side of 7edo), as well as because it is just below the diatonic "surface". | The name was coined by [[User:CompactStar|CompactStar]] in 2024. It refers to how it is an opposite to [[deeptone]] (which is on the other side of 7edo), as well as because it is just below the diatonic "surface". | ||
See [[Syntonic | See [[Syntonic–chromatic equivalence continuum#Shallowtone]] for technical data. | ||
== Interval chain == | == Interval chain == | ||
In the following table, prime harmonics are labeled in '''bold'''. | In the following table, prime harmonics are labeled in '''bold'''. | ||
{|class="wikitable" | |||
{| class="wikitable" | |||
|- | |- | ||
!rowspan="2"|# | ! rowspan="2" | # | ||
!rowspan="2"|Cents* | ! rowspan="2" | Cents* | ||
!colspan="2"|Approximate ratios | ! colspan="2" | Approximate ratios | ||
|- | |- | ||
!5-limit | ! 5-limit | ||
!13-limit extension | ! 13-limit extension | ||
|- | |- | ||
|0 | | 0 | ||
|0.000 | | 0.000 | ||
|[[1/1]] | | [[1/1]] | ||
| | | | ||
|- | |- | ||
|1 | | 1 | ||
|681.801 | | 681.801 | ||
|'''[[3/2]]''' | | '''[[3/2]]''' | ||
|[[13/9]] | | [[13/9]] | ||
|- | |- | ||
|2 | | 2 | ||
|163.602 | | 163.602 | ||
|[[9/8]] | | [[9/8]] | ||
|[[11/10]], [[13/12]], [[35/32]], [[81/70]], [[8192/8019]] | | [[11/10]], [[13/12]], [[35/32]], [[81/70]], [[8192/8019]] | ||
|- | |- | ||
|3 | | 3 | ||
|845.403 | | 845.403 | ||
|[[27/16]] | | [[27/16]] | ||
|'''[[13/8]]''', [[117/70]], [[4096/2673]] | | '''[[13/8]]''', [[117/70]], [[4096/2673]] | ||
|- | |- | ||
|4 | | 4 | ||
|327.204 | | 327.204 | ||
|[[81/64]] | | [[81/64]] | ||
|[[39/32]], [[99/80]], [[1024/891]] | | [[39/32]], [[99/80]], [[1024/891]] | ||
|- | |- | ||
|5 | | 5 | ||
|1009.0511 | | 1009.0511 | ||
|[[243/128]] | | [[243/128]] | ||
|[[117/64]], [[512/297]] | | [[117/64]], [[512/297]] | ||
|- | |- | ||
|6 | | 6 | ||
|490.806 | | 490.806 | ||
|[[512/405]], [[729/512]] | | [[512/405]], [[729/512]] | ||
|[[128/99]] | | [[128/99]] | ||
|- | |- | ||
|7 | | 7 | ||
|1172.607 | | 1172.607 | ||
|[[256/135]] | | [[256/135]] | ||
|[[64/33]] | | [[64/33]] | ||
|- | |- | ||
|8 | | 8 | ||
|654.408 | | 654.408 | ||
|[[64/45]] | | [[64/45]] | ||
|'''[[16/11]]''', [[112/81]] | | '''[[16/11]]''', [[112/81]] | ||
|- | |- | ||
|9 | | 9 | ||
|136.209 | | 136.209 | ||
|[[16/15]] | | [[16/15]] | ||
|[[12/11]], [[28/27]] | | [[12/11]], [[28/27]] | ||
|- | |- | ||
|10 | | 10 | ||
|818.010 | | 818.010 | ||
|'''[[8/5]]''' | | '''[[8/5]]''' | ||
|[[14/9]], [[18/11]] | | [[14/9]], [[18/11]], [[64/39]] | ||
|- | |- | ||
|11 | | 11 | ||
|299.811 | | 299.811 | ||
|[[6/5]] | | [[6/5]] | ||
|[[7/6]], [[27/22]], [[63/52]] | | [[7/6]], [[27/22]], [[63/52]] | ||
|- | |- | ||
|12 | | 12 | ||
|981.612 | | 981.612 | ||
|[[9/5]] | | [[9/5]] | ||
|'''[[7/4]]''', [[26/15]], [[81/44]] | | '''[[7/4]]''', [[26/15]], [[81/44]] | ||
|- | |- | ||
|13 | | 13 | ||
|463.413 | | 463.413 | ||
|[[27/20]] | | [[27/20]] | ||
|[[13/10]], [[21/16]], [[243/176]] | | [[13/10]], [[21/16]], [[243/176]] | ||
|- | |- | ||
|14 | | 14 | ||
|1145.214 | | 1145.214 | ||
|[[81/40]] | | [[81/40]] | ||
|[[39/20]], [[63/32]], [[729/352]] | | [[39/20]], [[63/32]], [[729/352]] | ||
|- | |- | ||
|15 | | 15 | ||
|627.015 | | 627.015 | ||
|[[243/160]] | | [[243/160]] | ||
|[[117/80]], [[189/128]] | | [[117/80]], [[189/128]] | ||
|} | |} | ||
<nowiki />* In 5-limit CTE tuning | |||
[[Category:Shallowtone| ]] <!-- main article --> | [[Category:Shallowtone| ]] <!-- main article --> | ||
[[Category:Rank-2 temperaments]] | |||
[[Category:Mint temperaments]] | [[Category:Mint temperaments]] | ||